Problem 106 - Introductory Algebra for College Students

Question

Write a rational expression that cannot be simplified.

Step-by-Step Solution

Answer

A rational expression that cannot be simplified is \( \frac {x} {x + 1} \).

Step 1: Pick the Numerator

Select a polynomial for the numerator. To keep things simple, choose \(p(x) = x\).

Step 2: Pick the Denominator

Now, select a polynomial for the denominator. Choose \(q(x) = x + 1\)

Step 3: Form the rational function

Combine the chosen polynomials in the form \( \frac {p(x)} {q(x)} \). Hence, the rational expression becomes \( \frac {x} {x + 1} \).

Step 4: Check if the fraction can be simplified

Check if there are any common factors between the numerator and the denominator that can be cancelled out. Since there are no common factors between the numerator x and the denominator x + 1, the fraction is in its simplest form.